Lena's crackers, one week: Every week the Mill Lane bakehouse makes crackers for cafés. Lena wants one picture of how they are doing.
The crackers' figures
- A packet sells for $2.50.
- Flour, butter and the packet cost $0.60 for each one made.
- The crackers carry $140 a week of the bakehouse's rent, oven and staff costs, whether Priti's team bakes ten packets or four hundred.
The picture should show, at a glance, how many packets a week the crackers must sell before they stop losing money, and how much they make when the cafés order 350.
That picture is a break-even chart: a graph of a product's total costs and its total revenue against the number of units made and sold (output). Where the two lines cross, revenue exactly covers costs: no profit and no loss. That crossing is the break-even point. It is the same idea as in 5.5.1: every packet's contribution of $1.90 chips away at the $140 of fixed costs until they are covered.
The shape of every break-even chart: fixed costs (FC) flat, total costs (TC) starting at fixed costs, total revenue (TR) starting at zero. Left of the break-even point (BEP) is a loss; right of it is a profit.
Interactive diagram
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What is drawn on the chart
Fixed costs line
A flat line at $140. Fixed costs do not change with output, so the line is the same height at 0 packets as at 400.
Total costs line (TC)
Starts at $140 on the vertical axis, because fixed costs are paid even when nothing is baked. It rises by $0.60 for every packet: total costs = fixed costs + variable cost per unit x output.
Total revenue line (TR)
Starts at zero, because no packets sold means no money in. It rises by $2.50 for every packet: total revenue = price x output.
Break-even point
Where the TR line crosses the TC line. Read down to the output axis for the break-even quantity, and across to the money axis for the revenue at that point.
| Part of the chart | What it shows | On Lena's chart |
|---|---|---|
| Vertical axis (y) | Money: costs and revenue, in dollars | Costs and revenue ($), from $0 to $1,000 |
| Horizontal axis (x) | Units made and sold | Output (packets of crackers a week), from 0 to 400 |
| The gap below the crossing | TC above TR: every output here makes a loss | Fewer than 74 packets a week |
| The gap above the crossing | TR above TC: every output here makes a profit | More than 74 packets a week |
Two lines, two starting points: The revenue line starts at the origin; the total costs line does not. At zero packets Lena still pays $140 of fixed costs, so total costs begin at $140.
A total costs line drawn from zero forgets the fixed costs and puts the break-even point in the wrong place, usually at zero.
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Both lines are straight, so each needs only two points: where it starts, at zero output, and where it ends, at the most the business could sell.
Work those out first, in a small table, before you pick up a ruler. Lena's cafés never take more than 400 packets a week, so her chart ends there.
| Output (packets a week) | Fixed costs | Total costs | Total revenue |
|---|---|---|---|
| 0 | $140 | $140 | $0 |
| 100 | $140 | $140 + $60 = $200 | $250 |
| 200 | $140 | $140 + $120 = $260 | $500 |
| 300 | $140 | $140 + $180 = $320 | $750 |
| 400 | $140 | $140 + $240 = $380 | $1,000 |
Constructing the chart, to scale
Choose the scale
Output axis from 0 to 400 packets, in equal steps of 50. Money axis from $0 to $1,000, the biggest number in the table, in equal steps of $100. Equal steps are what make it to scale.
Label both axes
Vertical: Costs and revenue ($). Horizontal: Output (packets of crackers). Both words, costs and revenue, belong on the vertical axis.
Draw total costs
With a ruler, from $140 on the vertical axis to $380 at 400 packets. Label it Total costs. A flat fixed costs line at $140 helps the reader, but the total costs line is the one that matters.
Draw total revenue
From the origin to $1,000 at 400 packets. Label it Total revenue, not Sales, which could mean packets rather than dollars.
Mark the break-even point
An arrow to the crossing, labelled Break-even point, or a dashed line from the crossing down to the output axis with the same label. On Lena's chart it sits at about 74 packets and $185.
Check the crossing with contribution: Each packet brings in $1.90 more than it costs to make (5.5.1). The week's $140 of fixed costs is covered after $140 divided by $1.90 = 73.7 packets, so by the 74th.
If your two lines cross far from 74 packets, one of them is drawn wrong. Recheck its two end points.
The chart is a drawing, not a list. A table of numbers, however correct, does not show where the lines cross. Draw it neatly, with a ruler, on the scale you chose, so that anyone can read a value off it and get the same answer you did.
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Three readings from one picture: Once the chart is drawn, Lena can read three things off it without another sum.
Three readings
- How many packets she must sell to break even.
- The profit or loss at any number of packets.
- How far sales could fall before the crackers start losing money.
Break-even quantity
- Go straight down from the crossing to the output axis
- Lena's crackers break even at 74 packets a week
- Read across to the money axis for the revenue there: about $185
Profit or loss at an output
- Go up from the output to both lines and measure the vertical gap between them
- At 350 packets: revenue $875, costs $350, so a profit of $525
- At 50 packets costs are above revenue: $170 against $125, a loss of $45
Margin of safety
- The horizontal gap on the output axis between break-even and actual sales
- Lena sells 350 packets and breaks even at 74, so 276 packets
- It is how far sales could fall before the crackers make a loss
Left of the crossing, the total costs line is above the revenue line: that wedge is the loss area. Right of it, revenue is above costs: the profit area, and it widens with every packet sold, by $1.90 each time. Many charts shade the two wedges and mark the margin of safety with a two-headed arrow along the output axis.
| The weekly chart | The same crackers over a year | |
|---|---|---|
| Fixed costs | $140 a week | $7,280 a year ($140 x 52 weeks) |
| Where the lines cross | 74 packets | 3,832 packets |
| Sales | 350 packets in a normal week | 18,000 packets in 2025 |
| Margin of safety | 350 - 74 = 276 packets | 18,000 - 3,832 = 14,168 packets |
Vertical is money, horizontal is packets: Profit or loss is read up and down, in dollars: the gap between the lines at one output. The margin of safety is read left to right, in units: the gap between two outputs.
Giving the margin of safety as $525, or the profit as 276 packets, mixes up the two directions.
How this comes up: The usual question: construct a fully labelled break-even chart, to scale, for four marks.
What the question gives and asks
- The table. The price, the variable cost per unit, the fixed costs (sometimes as a list of items to add up) and a maximum output or a sales forecast.
- Sometimes the chart is printed and you label its axes, for one mark.
- The parts that follow use the same figures for a profit or a margin of safety.
The four-mark pattern
- Both axes labelled. Vertical: costs and revenue ($). Horizontal: output, units, or the product's name.
- Total costs line. Starts at fixed costs on the vertical axis, ends at the correct total at the last output, labelled Total costs.
- Total revenue line. Starts at the origin, ends at price x the last output, labelled Total revenue.
- Break-even point. Marked where the two lines cross, with a labelled arrow or a labelled line down to the output axis.
Where charts lose their marks: A line from the wrong place. Total costs start at fixed costs, not at zero.
Half a label. A vertical axis that says only Costs, or a revenue line labelled Sales.
No scale. Freehand lines, uneven steps, or a table in place of a chart: a reader must be able to check every line against the numbers.
Construct a fully labelled break-even chart, to scale, for Lena's crackers for one week.
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.